Tyler's estimator performance analysis

Abstract

This paper analyzes the performance of Tyler's M-estimator of the scatter matrix in elliptical populations. We focus on non-asymptotic performance analysis of Tyler's estimator. Given n samples of dimension p <; n, we show that the squared Frobenius norm of the error of the inverse estimator is proportional to p2/(1-c2)2n with high probability, where c is the coherence coefficient of the properly scaled estimator. Under additional group symmetry conditions we improve the obtained bound, utilizing the inherent sparsity properties of group symmetry.